Balanced Manifolds and SKT Metrics

TL;DR

This paper investigates the relationship between balanced and Gauduchon cones on complex manifolds, showing their equality or inequality in various cases, and characterizing SKT manifolds in dimension three.

Contribution

It demonstrates the non-equality of these cones on twistor spaces, proves their equality on Moishezon manifolds, and characterizes certain SKT manifolds as Kahler.

Findings

Equality does not hold on many twistor spaces

Equality holds on Moishezon manifolds

SKT threefolds with equal cones are Kahler

Abstract

The equality between the balanced and the Gauduchon cones is discussed in several situations. In particular, it is shown that equality does not hold on many twistor spaces, and it holds on Moishezon manifolds. Moreover, it is proved that a SKT manifold of dimension three on which the balanced cone equals the Gauduchon cone is in fact Kahler.